Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the Owner Societies 2014 Supporting information Resonant Raman Spectra of Molecules with Diradical Character: Multiconfigurational Wavefunction Investigation of Neutral Viologens Julia Romanova, Vincent Liégeois, and Benoît Champagne * Laboratoire de Chimie Théorique, Unité de Chimie Physique Théorique et Structurale (UCPTS), University of Namur, Rue de Bruxelles 61, 5000 Namur, Belgium 1
Detailed analysis of Figure 1 Within the MP2 approach, the most intensive peak is mainly associated with the 0-0 transition (FC factor = 2.51E-01). The fundamental vibrational excitations of modes 10 (FC 9.58E- 02), 11 (FC 2.26E-02), and 29 (FC 4.31E-02), as well as the overtone 2ν 10 (FC 1.82E-02) also contribute this vibronic band. The peak at 378 nm represents the second most significant peak in the spectrum and its intensity is very close to the absorption maximum. This vibronic band mainly originated from the fundamental excitations of modes 63 (FC 8.51E-02) and 60 (FC 2.36E-02) and the simultaneous excitation of modes ν 10 +ν 63 (FC 3.24E-02). The next important contributions to the second peak come from the fundamental excitations of modes 34 (FC 2.08E-02), 39 (FC 1.54E- 02), and 43 (FC 1.92E-02), but also from the combinations of bands ν 10 +ν 29 (FC 1.64E-02) and ν 29 +ν 63 (FC 1.46E-02). The shoulder at 350 nm is associated mostly with the overtone 2ν 63 (FC 1.44E-02) but also with several combinations of bands: ν 60 +ν 63 (FC 7.99E-03), ν 10 +2ν 63 (FC 5.48E- 03) and ν 10 +ν 60 +ν 63 (FC 3.05E-03). Within the CASSCF approach, the single vibronic band peaking at 378 nm originates from the 0-0 transition (FC 1.22 E-01) as well as from fundamental excitations of modes 29 (FC 8.92E- 02), 63 (FC 3.19E-02), 10 (FC 2.54E-02), 46 (FC 2.24 E-02) and from the overtone 2ν 29 (FC 3.27E- 02). 2
Table S1. Optimized bond lengths, R [Å] and dihedral angles θ [ ] for the ground state of methyl viologen in different oxidation states as determined at different levels of approximation. MV 0 MV 0 MV 2+ MV + MV 0 SS-CASSCF (14,12) SS-CASSCF (10,10) MP2 MP2 MP2 R(Me-N 1 ) 1.446 1.446 1.491 1.469 1.456 R(N 1 -C 1 ) 1.391 1.395 1.355 1.368 1.393 R(C 1 -C 2 ) 1.350 1.349 1.390 1.373 1.362 R(C 2 -C 3 ) 1.467 1.469 1.403 1.429 1.453 R(C 3 -C 3 ') 1.374 1.372 1.482 1.433 1.391 Table S2. SA2-CASSCF vertical excitation energy E 0e [ev], wavelength λ 0e [nm] and transition dipole moment µ 0e [a.u.] of PEV 0. The SA2-CASPT2 values of PEV 0 are obtained by correcting the SA2-CASPT2 results of MV 0 for the effect of the phenylene extension, as determined at the SA2- CASSCF level [ E phenylene = 4.68(PEV 0 ) - 5.65(MV 0 ) = -0.97 ev]. SA2-CASSCF SA2-CASPT2 Ε 0e 4.68 2.31 λ 265 537 µ 4.23 Used for the simulations of RR and absorption spectra. 3
Table S3. Mode labels, vibrational frequencies ω l [cm -1 ], and Huang-Rhys factors S l for the 1 st excited state of MV 0 and PEV 0 calculated with the MP2 and SS-CASSCF methods. Only the normal modes with S l >0.005 are displayed. MV 0 PEV 0 MP2 SS-CASSCF MP2 ω sc.* S l ω sc.* S l ω sc.* S l 241 0.393 270 0.035 58 0.025 277 0.093 291 0.229 63 0.032 469 0.018 652 0.172 70 0.188 668 0.012 766 0.803 109 0.317 791 0.177 852 0.020 218 0.132 812 0.008 976 0.124 268 0.449 994 0.085 1139 0.042 293 0.008 1133 0.063 1200 0.080 335 0.738 1215 0.079 1245 0.202 384 0.007 1254 0.028 1467 0.027 390 0.014 1389 0.010 1489 0.008 418 0.012 1451 0.007 1548 0.150 431 0.136 1545 0.097 1659 0.287 492 0.098 1660 0.349 536 0.019 570 0.007 743 0.074 947 0.063 987 0.120 998 0.015 1234 0.154 1363 0.066 1472 0.108 1487 0.009 1565 0.107 1658 0.168 * Scaling factor 0.970 **Scaling factor 0.912 4
Figure S1. Initial guess for CASSCF calculation on MV0 (right) and PEV0 (left). The molecular symmetry of PEV0 and MV0 is C2v obtained with the RHF/STO-3G method. 5
Natural orbitals occupation numbers (ON) from SS-CASSCF(10,10) calculation on the MV 0 ground state: 3 MOs in a 1 (16, ON=1.95; 17, ON=1.85; 18, ON=0.06) 3 MOs in b 1 (15, ON=1.93; 16, ON=0.13; 17, ON=0.04) 2 MOs in b 2 (9, ON=1.92; 10, ON=0.08) 2 MOs in a 2 (9, ON=1.92; 10, ON=0.08). Natural orbitals occupation numbers (ON) from SA2-CASSCF(10,10) calculation on the MV 0 : 3 MOs in a 1 (16, ON=1.96; 17, ON=1.42; 18, ON=0.06) 3 MOs in b 1 (15, ON=1.93; 16, ON=0.56; 17, ON=0.03) 2 MOs in b 2 (9, ON=1.92; 10, ON=0.08) 2 MOs in a 2 (9, ON=1.92; 10, ON=0.08). Major contributions in the CI vectors from SA2-CASSCF(10,10) calculation on the MV 0 : S 0 22222 00000 0.90 22220 20000-0.16 S 1 2222a b0000-0.65 2222b a0000 0.65 6
Natural orbitals occupation numbers (ON) from SS-CASSCF(16,16) calculation on the PEV 0 ground state: 5 MOs in a 1 (17, ON=1.96; 19, ON=1.93; 20, ON=1.77; 21, ON=0.10; 22, ON=0.05) 5 MOs in b 1 (17, ON=1.95; 18, ON=1.90; 19, ON=0.23; 20, ON=0.06; 22, ON=0.04) 3 MOs in b 2 (12, ON=1.92; 13, ON=1.91; 14, ON=0.09) 3 MOs in a 2 (11, ON=1.92; 12, ON=0.09; 13, ON=0.09). Natural orbitals occupation numbers (ON) from SA2-CASSCF(16,16) calculation on the PEV 0 : 5 MOs in a 1 (17, ON=1.96; 19, ON=1.94; 20, ON=1.36; 21, ON=0.11; 22, ON=0.04) 5 MOs in b 1 (17, ON=1.95; 18, ON=1.91; 19, ON=0.62; 20, ON=0.06; 22, ON=0.03) 3 MOs in b 2 (12, ON=1.92; 13, ON=1.92; 14, ON=0.09) 3 MOs in a 2 (11, ON=1.92; 12, ON=0.09; 13, ON=0.08). Major contributions in the CI vectors from SA2-CASSCF(16,16) calculation on the PEV 0 : S 0 22200 220 22000 200 0.814 22000 220 22200 200-0.214 S 1 22b00 220 22a00 200-0.607 22a00 220 22b00 200 0.607 7
Figure S2. MV + (left) and MV 0 (right) UV/vis absorption spectra from T. M. Bockman and J. K. Kochi, J. Org. Chem., 1990, 55, 4127. 8
Figure S3. (Top) RR spectra of MV0 simulated by using SA2-CASSCF ground and excited state geometries together with MP2 (A) and SS-CASSCF (B) ground state vibrational normal modes. The energy of the incident light was to E0e+0.30 ev in order to match the experimental 363.8 nm wavelength. The Raman bands are represented by Lorentzian functions with FWHM set to 10 cm-1. (Bottom) Experimental RR spectrum of MV in different oxidation states. (d) corresponds to the RR spectrum of MV0 prepared by electrolysis in acetonitrile solution, recorded at exciting laser wavelength 363.8 nm from Q. Feng and T. M. Cotton, J. Phys. Chem., 1986, 90, 983. 9